I think when we first begin our HHJ that we take all advice, suggestions, etc. as hard-fast rules. If it works for you then there should be no reason to stop using it. Early into my HHJ, I stopped using anything with sulfates, mineral oil, or petroleum. I've found that shampoos with sulfates do NOT strip my hair of moisture - or at least not a significant amount.
To answer your question though - lol - mineral oil/petroleum are still culprits to me. It makes my hair feel icky and I haven't had too much trouble finding moisturizing products that do not contain them.